Galaxy Clusters and Large Scale Structure

1
Galaxy Clusters and Large Scale Structure

• (Also topics will touch on gravitational lensing
  and dark matter)
• Unless noted, all figuress and equations from
  the textbooks Combes et al. Galaxies and
  Cosmology or Longairs Galaxy Formation.

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Galaxy Clusters

• Galaxy Clusters
• Cluster Masses
• Dynamical, X-ray, and from Lensing
• Dark Matter
• Large Scale Structure

3
Cluster Catalogs

• Palomar Sky Survey using 48 inch Schmidt
  telescope (1950s)
• Abell (1958) cataloged rich clusters a famous
  work and worth a look
• Abell, Corwin, Olowin (1989) did the same for
  the south using similar plates
• All original work was by visual inspection

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Pavo Cluster
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Cluster Selection Criteria (Abell)

• Richness Criterion 50 members brighter than 2
  magnitudes fainter than the third brightest
  member. Richness classes are defined by the
  number in this range

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Cluster Selection Criteria (Abell)

• Compactness Criterion Only galaxies within an
  angular radius of 1.7/z arcmin get counted. That
  corresponds to a physical radius of 1.5 h-1 Mpc.
  The redshifts are (were) estimated based on the
  apparent magnitude of the 10th brightest cluster
  member.

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Cluster Selection Criteria (Abell)

• Distance Criteria Lower redshift limit (z
  0.02) to force clusters onto 1 plate. Upper
  limit due to mag limit of POSS, which matches z
  of about 0.2. Distance classes based on
  magnitude of 10th member

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More on Abell Clusters

• Complete Northern Sample
• 1682 Clusters of richness 1-5, distance 1-6.
• Counts in Table 4.2 follow
• This is consistent with a uniform distribution.
• Space Density of Abell Clusters richer than 1
• For uniform distribution, cluster centers would
  be 50 h-1 Mpc apart, a factor of ten larger than
  that of mean galaxies.

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Clusters of Clusters

• Based on Abells Northern Sample
• Spatial 2-point correlation function (Bahcall)
• Scale at which cluster-cluster correlation
  function has a value of unity is 5 times greater
  than that for the galaxy-galaxy correlation
  function.

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Clusters of Clusters

• Peebles (1980) schematic picture
• Cloud of galaxies is basic unit, scale of 50 h-1
  Mpc
• About 25 of galaxies in these clouds
• All Abell Clusters are members of clouds (with
  about 2 per cloud), and contain about 25 of the
  galaxies in a cloud are in Abell Clusters
  (superclusters occur when several AC combine)
• Remaining 75 follow galaxy-galaxy function
• In terms of larger structures, galaxies hug the
  walls of the voids, clusters at the intersections
  of the cell walls.

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Galaxies within Clusters

• A range of structural types (Abell)
• Regular indicates cluster is circular, centrally
  concentrated (cf. Globular clusters), and has
  mostly elliptical and S0 galaxies. Can be very
  rich with 1000 galaxies. Coma is regular.
• All others are irregular (e.g., Virgo).
• I dont know why he didnt just call them type 1
  and type 2! /sarcasm

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Galaxies within Clusters

• A range of structural types (Oemler 1974)
• cD clusters have 1 or 2 central dominant cD
  galaxies, and no more than about 20 spirals,
  with a E S0 S ratio of 3 4 2.
• Spiral-rich clusters have E S0 S ratios more
  like 1 2 3 about half spirals.
• Remainder are spiral-poor clusters. No dominant
  cD galaxy and typical ratio of 1 2 1.

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Galaxies within Clusters

• Galaxies differ in these types (Abell)
• In cD clusters galaxy distribution is very
  similar to star distribution in globular
  clusters.
• Spiral-rich clusters and irregular clusters tend
  not to be symmetric or concentrated.
• Spiral-poor clusters are intermediate cf. above.
• In spiral rich clusters, all galaxy types
  similarly distributed and no mass segregation,
  but in cD and spiral-poor clusters, you dont see
  spirals in the central regions where the most
  massive galaxies reside.

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Structures of Regular Clusters

• Bahcall (1977) describes distributions as
  truncated isothermal distributions
• Where f(r) is the projected distribution
  normalized to 1 at r0, and C is a constant that
  makes N(r) 0 at some radius. Results in
  steepening distribution in outer regions vs. pure
  isothermal soultion.
• R1/2 150-400 kpc (220 kpc for Coma)

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Structures of Regular Clusters

• In central regions King profiles work well
• For these distributions N0 2Rc?0.
• De Vaucouleurs law can also work.
• Problem is observations do not constrain things
  quite tightly enough.

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Rich Cluster Summary
B-M Class I have central cD galaxy, Class III do
not.
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Rich Cluster Summary
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Dark Matter in Galaxy Clusters

• How do we know it is there?
• Dynamical estimates of cluster masses
• X-ray emission/masses
• (Sunyaev-Zeldovich Effect)
• Gravitational lensing!
• What is the dark matter???
• Baryons vs. non-Baryons

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Dynamical Masses

• Virial Theorem A relationship between
  gravitational potential energy and velocities for
  a dynamically relaxed and bound system.
• Ellipticals not necessarily rotating.
• T ½ U, where T is the total kinetic energy
  and U is the potential energy.
• So, for a cluster of stars or a cluster of
  galaxies, measuring T (by measuring velocities)
  can give U and therefore M.

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Galaxy Masses

• Virial Theorem T ½ U
• You do need to worry about the conditions of the
  theorem in an astrophysical context. For
  instance, comparing crossing times with the
  relevant timescale. Text examples are the suns
  orbital period and galaxies in Coma.

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Derivation of Virial Theorem
Tensor virial theorem for a self-gravitating
system of collisionless point masses. Cf. Binney
Tremaine 1987.
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Galaxy Masses

• Astronomical context more complex. Cannot in
  general get all the 3D velocities. In exgal
  context, uncertain cosmology can translate into
  uncertain spatial dimensions. Usually only have
  position on sky plus radial velocities. Must
  make assumptions about velocity distribution to
  apply virial theorem.

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Masses

• Isotropic case 3 (why?)
• If velocity dispersion independent of masses
• T 3/2 M , where M is total mass
• More complex if the above is not true. Assuming
  spherical symmetry and an observed surface
  distribution, get a weighted mean separation Rcl

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Dark Matter in Galaxy Clusters

• Dynamical estimates of cluster masses
• Virial Theorem as we have discussed, but
• Very few clusters exist that can be well done!
• E.g, which are cluster members?
• Must measure many velocities
• Case of Coma
• Regular rich cluster, looks like isothermal
  sphere
• Crossing time arguments OK
• Virial mass issue for Coma first by Zwicky (1937)
• Surface distribution, velocities in next figure

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Dynamic Properties of Coma
King model fit in top panel. Projected
velocities vs anglular radius. Bottom shows
three consistent velocity dipsersion profiles,
vs. radius now.
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Dynamic Masses for Coma

• Merritt (1987) analysis
• Assuming constant M/L ratio, then mass is 1.79 x
  1015h-1 solar masses, and M/L is 350 h-1 in solar
  units (think about that!).
• Typical M/L for ellipticals is 15 in solar units.
• Differ by a factor of 20
• Why should the dark matter have the same
  distribution as the light?
• Why should the velocities even be isotropic?

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X-ray Masses for Clusters

• UHURU in 1970s
• Rich clusters very bright in X-rays!
• Bremsstrahlung emission of hot intercluster gas
• Very hot gas requires large potential to hold
• Can use to estimate the cluster mass

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein (1980, ApJ 241,
  552)
• Assume spherical symmetry (as usual!)
• Assume hydrostatic equilibrium (yes!)
• Perfect gas law

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein
• For ionized gas, cosmic abundances, µ 0.6
• Differentiating the gas law, and inserting into
  the hydrostatic equation
• So, the mass distribution can be found if the
  variation of pressure and temperature with radius
  are known (measured).

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein
• Bremsstrahlung spectral emissivity
• Gaunt factor can be approximated

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X-ray Masses for Clusters

• Fabricant, Lecar, and Gorenstein
• Bremsstrahlung spectrum is roughly flat up to
  X-ray energies, above which it cuts off
  exponentially. Cut-off is related to
  temperature. E h? kBT. The measurement is a
  projection onto 2D space. Integrating emissivity
  and converting to intensity (surface brightness
  at the projected radius a)

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X-ray Masses for Clusters

• Simplified procedure
• Luminosity Density total energy per second per
  unit volume integrating over all frequencies, for
  a fully ionized hydrogen plasma
• Lvol 1.42 x 10-27ne2T1/2 ergs/s/cm3
• Sometimes it can be assumed that you have an
  isothermal sphere (which is the case when the
  dark matter and the gas have the same radial
  dependence).

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X-ray Masses for Clusters

• So, from the spectrum we can get the temperature
  as a function of radius, and from the intensity
  we can get the emissivity and hence the particle
  density.
• Chandra is great for this type of observation
• http//chandra.harvard.edu/photo/2002/0146/
• http//chandra.harvard.edu/photo/0087/
• http//www1.msfc.nasa.gov/NEWSROOM/news/photos/200
  2/photos02-037.html

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Chandra Images of Clusters
Abell 1689, Optical X-rays
Abell 2125, X-rays only
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X-ray Masses for Clusters

• ROSAT pictures old and busted.
• Chandra images The New Hotness.
• Important result is that the dark matter does
  follow the galaxies.
• Typical masses then are 5x1014-15 solar masses,
  only 5 visible light, 10-30 hot gas, rest is
  DM.

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Forms of Dark Matter???

• Were certain it is present (Bullet Cluster and
  newer observations nail it) A Direct Empirical
  Proof of the Existence of Dark Matter. Clowe, D.,
  Bradac, M., Gonzalez, A. H., Markevitch, M,
  Randall, S., Jones, C., Zaritsky, D. 2006, ApJ
  Letters, 648, 109
• Some is baryonic (1/6).
• Most is non-baryonic (5/6), WIMPs

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Large Scale Structure

• Galaxy structure how is the mass in the
  universe distributed (and recall gas can be
  important, too!)? Homogeneous? On what scale?
• Current best work is the SDSS
• Background radiation also of interest (discrete
  sources vs. true diffuse background).

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Background SED

• CMBR of special interest (as we will get to) and
  X-ray is a recent development (CXO).

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The Third Dimension

• Galaxy distributions seen in images are 2-d
  projections on the sky.
• Need distanceseasiest way is to use the Hubble
  flow and redshifts, either photometric or spectra
  (best).
• Reminder SDSS and 2dF rule here now.
• Huchra and Gellars Z-machine for the CfA
  survey as recounted in Lonely Hearts of the
  Cosmos by Dennis Overbye Great!

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The Third Dimension

• Look at distance slices here.

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The Third Dimension

• The famous man in the distribution. Shows
  walls, voids, etc.
• Why elongations, finger of god distributions
  pointing at us?

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Statistical Methods

• Correlation functions
• How do you measure, quantitatively, the tendency
  of galaxies to cluster?
• Following is specifically from Longair, but also
  present in Combes et al. with a different
  presentation.

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Large-scale Distribution of Galaxies
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Large-scale Distribution of Galaxies

• On small scales, the universe is very
  inhomogeneous (stars, galaxies). What about
  larger scales?
• Angular two-point correlation function w(?)

Where w(?) represents the excess probability of
finding a galaxy at an angular distance ? from
another galaxy. dO is a solid angle element. ng
is the average galaxy surface density.
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Large-scale Distribution of Galaxies

• This function w(?) describes apparent clustering
  on the sky down to some magnitude limit.
• More physically meaningful is the spatial
  two-point correlation function ?(r) which
  describes clustering in 3-D about a galaxy

• Now N(r) dV describes the number of galaxies in
  the volume element dV at a distance r from any
  galaxy. No is another normalization factorv
  (ave.).

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Large-scale Distribution of Galaxies

• w(?) isnt so hard to measure from various
  surveys just need positions.
• ?(r) is harder must have redshifts to do
  properly. Can make some assumptions however.

• Observationally verified parameterization works
  for scales of 100 h-1 kpc to 10 h-1 Mpc, and you
  get r0 5 h-1 Mpc and ? 1.8. Note use of h.

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Large-scale Distribution of Galaxies

• Maddox et al. (1990)

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Large-scale Distribution of Galaxies

• Points to consider with regard to the two-point
  correlation studies
• Galaxies appear to be sampled from a homogeneous
  but clustered distribution.
• Clustering appears over a wide range of scales.
• No clearly preferred scales.
• Clustering drops off more rapidly on largest
  scales (smooths out, essentially isotropic).

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Large-scale Distribution of Galaxies
3D distribution from Geller and Huchra 1989
(using the z-machine). Some 14000
galaxies. Holes up to about 50/h Mpc in
size. Spongelike
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Large-scale Distribution of Galaxies
Las Campanas Redshift Survey, 4 times greater
distances than Harvard. Over 26,000 galaxies.
Similar results, with same scales for clumping,
etc.
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Large-scale Distribution of Galaxies
Brightest galaxies in the sky. Note local
supercluster.
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Large-scale Distribution of Galaxies
Slices through the 3-dimensional map of the
distribution of galaxies from the Sloan Digital
Sky Survey (SDSS). The earth is at the center,
and each point represents a galaxy, typically
containing about 100 billion stars. Galaxies are
colored according to the ages of their stars,
with the redder, more strongly clustered points
showing galaxies that are made of older stars.
The outer circle is at a distance of two billion
light years. The region between the wedges was
not mapped by the SDSS because dust in our own
Galaxy obscures the view of the distant universe
in these directions. The lower slice is thinner
than the upper slice, so it contains fewer
galaxies. Credit M. Blanton and the SDSS.
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Large-scale Distribution of Galaxies
Distribution of 31000 brightest radio sources (6
cm).
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Large Scale Motions

• Milky Way motion vs. CMBR, a dipole with
  velocity of about 1000 km/s (from COBE)

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Large Scale Motions

• The Great Attractor

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Large-scale Distribution of Galaxies
Simulations were performed at National Center
for Supercomputer Applicationsby Andrey Kravtsov
(The University of Chicago) and Anatoly Klypin
(New Mexico State University).